geometry-labs

More documents

Recommendations

Info

LAB 4.2 Polyominoes and Symmetry (continued) Name(s) Discussion A. Which types of symmetry in Problem 2 have no polyomino examples Why B. How are the answers to Problem 1 and Problem 2 related C. Imagine that polyominoes were one-sided (like tiles) and that you could not flip them over.Then there would have to be, for example, separate pentominoes for the shapes L and . In other words, there would be more polyominoes. Find all the additional polyominoes you would need in order to have a full set for areas 1 to 5. L 56 Section 4 Polyominoes Geometry Labs © 1999 Henri Picciotto, www.MathEducationPage.org
LAB 4.3 Polyomino Puzzles Name(s) Equipment: 1-Centimeter Grid Paper, interlocking cubes 1. Using interlocking cubes, make a set of all of the polyominoes with area 2, 3, and 4. You should have eight pieces. It is best to make each polyomino a single color. 2. On graph paper, draw all the rectangles (including squares) that satisfy these two conditions. • They have area 28 or less. • Their dimensions are whole numbers greater than 1. 3. Use the polyominoes you made in Problem 1 to cover the rectangles you drew in Problem 2.The 2 3 rectangle, covered by a domino and l tetromino, is shown in the figure at right. Record your solutions. Note: One rectangle is impossible with this set of polyominoes. 4. On Centimeter Grid Paper, draw staircases like the ones in the figures at right, with area between 3 and 28, inclusive. Cover each one with some of the polyominoes you made in Problem 1, and record your solutions. Discussion A. Describe your system for finding all the rectangles in Problem 2. B. Which rectangle puzzle cannot be solved in Problem 3 Why C. Find a formula for the area of a staircase like the two-step and three-step examples in Problem 4, given that it has x steps. Geometry Labs Section 4 Polyominoes 57 © 1999 Henri Picciotto, www.MathEducationPage.org
Page 1:
GEOMETRY Henri Picciotto LABS ACTIV
Page 4 and 5:
Project Editor: Editorial Assistant
Page 7 and 8:
Contents Introduction .............
Page 9 and 10:
9 Distance and Square Root ........
Page 11 and 12:
Introduction About This Book This b
Page 13 and 14:
• Manipulatives can motivate stud
Page 15 and 16:
If you have access to computers, I
Page 17 and 18:
1 Angles An essential foundation of
Page 19 and 20:
LAB 1.1 Angles Around a Point Name(
Page 21 and 22: LAB 1.2 Angle Measurement (continue
Page 23 and 24: LAB 1.4 Angles of Pattern Block Pol
Page 25 and 26: LAB 1.5 Angles in a Triangle Name(s
Page 27 and 28: LAB 1.6 The Exterior Angle Theorem
Page 29 and 30: LAB 1.6 The Exterior Angle Theorem
Page 31 and 32: LAB 1.7 Angles and Triangles in a C
Page 33 and 34: LAB 1.8 The Intercepted Arc (contin
Page 35 and 36: LAB 1.10 Soccer Angles Name(s) Equi
Page 37 and 38: LAB 1.10 Soccer Angles (continued)
Page 39 and 40: LAB 1.10 Soccer Angles (continued)
Page 41 and 42: 2 Tangrams Tangram puzzles are quit
Page 43 and 44: LAB 2.1 Meet the Tangrams (continue
Page 45 and 46: LAB 2.2 Tangram Measurements (conti
Page 47 and 48: LAB 2.4 Symmetric Polygons Name(s)
Page 49 and 50: 3 Polygons In the first two labs, t
Page 51 and 52: LAB 3.1 Triangles from Sides (conti
Page 53 and 54: LAB 3.2 Triangles from Angles (cont
Page 55 and 56: LAB 3.3 Walking Convex Polygons (co
Page 57 and 58: LAB 3.4 Regular Polygons and Stars
Page 59 and 60: LAB 3.5 Walking Regular Polygons (c
Page 61 and 62: LAB 3.6 Walking Nonconvex Polygons
Page 63 and 64: LAB 3.8 Sum of the Angles in a Poly
Page 65 and 66: LAB 3.9 Triangulating Polygons (con
Page 67 and 68: 4 Polyominoes Polyominoes are a maj
Page 69 and 70: LAB 4.1 Finding the Polyominoes Nam
Page 71: LAB 4.2 Polyominoes and Symmetry Na
Page 75 and 76: LAB 4.4 Family Trees (continued) Na
Page 77 and 78: LAB 4.5 Envelopes (continued) Name(
Page 79 and 80: LAB 4.7 Minimum Covers Name(s) Equi
Page 81 and 82: LAB 4.9 Polytans Name(s) Equipment:
Page 83 and 84: LAB 4.10 Polyrectangles (continued)
Page 85 and 86: 5 Symmetry Many of the activities i
Page 87 and 88: LAB 5.1 Introduction to Symmetry (c
Page 89 and 90: LAB 5.2 Triangle and Quadrilateral
Page 91 and 92: LAB 5.3 One Mirror Name(s) Equipmen
Page 93 and 94: LAB 5.4 Two Mirrors Name(s) Equipme
Page 95 and 96: LAB 5.4 Two Mirrors (continued) Nam
Page 97 and 98: LAB 5.5 Rotation Symmetry (continue
Page 99 and 100: LAB 5.6 Rotation and Line Symmetry
Page 101 and 102: LAB 5.7 Two Intersecting Lines of S
Page 103 and 104: LAB 5.8 Parallel Lines of Symmetry
Page 105 and 106: Triangles and 6Quadrilaterals The c
Page 107 and 108: LAB 6.1 Noncongruent Triangles (con
Page 109 and 110: LAB 6.2 Walking Parallelograms (con
Page 111 and 112: LAB 6.4 Making Quadrilaterals from
Page 113 and 114: 7 Tiling In this section, we addres
Page 115 and 116: LAB 7.1 Tiling with Polyominoes Nam
Page 117 and 118: LAB 7.2 Tiling with Pattern Blocks
Page 119 and 120: LAB 7.4 Tiling with Regular Polygon
Page 121 and 122: 8 Perimeter and Area This section s
Page 123 and 124:
LAB 8.1 Polyomino Perimeter and Are
Page 125 and 126:
LAB 8.2 Minimizing Perimeter Name(s
Page 127 and 128:
LAB 8.3 A Formula for Polyomino Per
Page 129 and 130:
LAB 8.4 Geoboard Area Name(s) Equip
Page 131 and 132:
LAB 8.5 Geoboard Squares Name(s) Eq
Page 133 and 134:
LAB 8.6 Pick’s Formula (continued
Page 135 and 136:
Distance and 9Square Root This chap
Page 137 and 138:
LAB 9.1 Taxicab Versus Euclidean Di
Page 139 and 140:
LAB 9.2 The Pythagorean Theorem Nam
Page 141 and 142:
LAB 9.3 Simplifying Radicals Name(s
Page 143 and 144:
LAB 9.4 Distance from the Origin Na
Page 145 and 146:
LAB 9.6 Taxicab Geometry Name(s) Eq
Page 147 and 148:
10 Similarity and Scaling Similarit
Page 149 and 150:
LAB 10.1 Scaling on the Geoboard Na
Page 151 and 152:
LAB 10.2 Similar Rectangles Name(s)
Page 153 and 154:
LAB 10.3 Polyomino Blowups Name(s)
Page 155 and 156:
LAB 10.3 Polyomino Blowups (continu
Page 157 and 158:
LAB 10.5 3-D Blowups Name(s) Equipm
Page 159 and 160:
LAB 10.6 Tangram Similarity Name(s)
Page 161 and 162:
LAB 10.7 Famous Right Triangles Nam
Page 163 and 164:
11 Angles and Ratios This section p
Page 165 and 166:
LAB 11.1 Angles and Slopes Name(s)
Page 167 and 168:
LAB 11.2 Using Slope Angles Name(s)
Page 169 and 170:
LAB 11.3 Solving Right Triangles Na
Page 171 and 172:
LAB 11.4 Ratios Involving the Hypot
Page 173 and 174:
LAB 11.5 Using the Hypotenuse Ratio
Page 175 and 176:
Trigonometry Reference Sheet The pa
Page 177 and 178:
LAB 11.6 The Unit Circle (continued
Page 179 and 180:
LAB 11.7 Name(s) Perimeters and Are
Page 181 and 182:
LAB 11.8 “” for Regular Polygon
Page 183 and 184:
1 Angles Lab 1.1: Angles Around a P
Page 185 and 186:
For this pattern block hexagon, add
Page 187 and 188:
Theorems: triangle sum theorem, iso
Page 189 and 190:
Answers 1-5. See student work. 6. T
Page 191 and 192:
7. Answers will vary. Discussion An
Page 193 and 194:
compass and straightedge.You may al
Page 195 and 196:
3. Answers will vary. Here are some
Page 197 and 198:
which Question B hints at, is that
Page 199 and 200:
To make an algebra connection, you
Page 201 and 202:
Answers 1. See Polyomino Names Refe
Page 203 and 204:
Answers 1. C. F, N, P D. Only the W
Page 205 and 206:
Lab 4.7: Minimum Covers This lab is
Page 207 and 208:
5. Discussion Answers A. Polyominoe
Page 209 and 210:
information in the relevant cells o
Page 211 and 212:
Discussion Answers A. Pentagons and
Page 213 and 214:
other. Students can make rubber sta
Page 215 and 216:
draw the lines and duplicate them y
Page 217 and 218:
5. Answers will vary. Here are some
Page 219 and 220:
Or students could analyze: • poss
Page 221 and 222:
For Problem 2, make sure the studen
Page 223 and 224:
2 hexagons, 2 triangles 1 hexagon,
Page 225 and 226:
4. P max 2A 2 5. Answers will vary.
Page 227 and 228:
This shows that 2 A⎤ 2n, and sinc
Page 229 and 230:
Lab 8.5: Geoboard Squares Prerequis
Page 231 and 232:
Answers 1. a. 11 b. 10 c. 4 d. 6.4
Page 233 and 234:
3. Discussion Answers A. √5 5 √
Page 235 and 236:
If your students enjoy Problem 6, a
Page 237 and 238:
4. a. 5. a. (0, 0) (6, 0) (0, 0) (0
Page 239 and 240:
congruent to each other and similar
Page 241 and 242:
2. (In the Perimeter table, numbers
Page 243 and 244:
Discussion Answers A. They are the
Page 245 and 246:
Discussion Answers A. Each individu
Page 247 and 248:
3. Triangle c: 1, 3, 2 4. Triangles
Page 249 and 250:
type of slope triangle will work fo
Page 251 and 252:
Discussion Answers A. Answers will
Page 253 and 254:
8. sin 2 cos 2 1. It is the Pythago
Page 255 and 256:
Geometry Labs Geoboard Paper 239 ©
Page 257 and 258:
Geometry Labs 1-Centimeter Grid Pap
Page 259 and 260:
Geometry Labs Circle Geoboard Paper
Page 261 and 262:
To make the radius of this circle e
Page 263 and 264:
Geometry Labs Unit Circles 247 © 1
Page 266:
GEOMETRY LABS Geometry Labs are han
show all

geometry-labs

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?